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The solution to the system of linear equations is:

\[
x = -10
\]
\[
y = 20
\]
\[
z = -40
\]
\[
w = 12
\]

Would you like further details on how this was solved, or do you have any questions?

Here are 5 related questions for you to consider:
1. How would the solution change if one of the constants were modified?
2. Can the solution be verified using a different method, such as substitution?
3. How does matrix factorization help solve systems of equations like this one?
4. What are the implications of having no solution or infinite solutions in such a system?
5. How does the determinant of the coefficient matrix affect the solvability of the system?

**Tip:** If the determinant of the coefficient matrix is zero, the system might either have no solutions or infinitely many solutions (i.e., it is dependent).

Use a software program or a graphing utility to solve the system of linear equations: 
0.2x - 2.3y + 1.4z - 0.55w = -110.6
3.4x + 1.3y - 1.7z + 0.45w = 65.4
0.5x - 4.9y + 1.1z - 1.6w = -166.2
0.6x + 2.8y - 3.4z + 0.3w = 189.6

This example demonstrates solving a system of four linear equations with four variables using techniques from linear algebra. The solution for the variables is: x = -10, y = 20, z = -40, w = 12. This problem involves key concepts such as matrix operations, Gaussian elimination, and determinants.

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